Tuesday, October 02, 2012

A monetary policy pop quiz

I freely admit that I don't understand monetary policy incredibly well. Sure, I solved some New Keynesian models in my field classes. I remember what happens in equilibrium. And I taught intro macroeconomics a few times, and learned all the standard kiddie models - money demand, loanable funds, AD-AS, long-run and short-run Phillips curves. I saw the "Friedman Rule" derived a couple times. But there is much about monetary policy I don't understand. First, I don't understand all of the particulars of how monetary policy is actually conducted. Second, I don't have much intuition for what happens far away from the equilibria in most models, especially if the equations that define the equilibrium are not linearized. Finally, I do not understand what would happen if this or that assumption of the models I know were dropped, or how plausible alternative, non-mainstream models are. All I know, really, are: A) the linearized equilibria of New Keynesian sticky-price models, similar models like Mankiw's "sticky information" models, B) some "New Classical" models like the Lucas Islands and RBC models, and C) some heuristics and hand-wavey ideas from the age of Milton Friedman and Paul Samuelson.

[I]f the FOMC maintains the fed funds rate at its current level of 0-25 basis points for too long, both anticipated and actual inflation have to become negative. Why? It’s simple arithmetic. Let’s say that the real rate of return on safe investments is 1 percent and we need to add an amount of anticipated inflation that will result in a fed funds rate of 0.25 percent. The only way to get that is to add a negative number—in this case, –0.75 percent.

To sum up, over the long run, a low fed funds rate must lead to consistent—but low—levels of deflation.

Is this right? Do permanently low interest rates eventually lead to permanent deflation? My instincts say that this cannot be true. My instincts say that printing more money cannot lead to deflation at long time scales - if you wait long enough, an increase in the supply of money will decrease money's value.

So what would happen if the Fed kept interest rates at zero forever? Would inflation rise to a new, higher average level and stay there, or would it keep accelerating until hyperinflation resulted and the real interest rate plunged to negative infinity? I'm not sure.

OK, so let's think about the opposite policy. What if the Fed tried to keep the nominal interest rate at, say, 50% forever? First of all, could it do that, or would it empty out its balance sheet and have to give up, like an emerging market trying to maintain a currency peg? And if a 50% real interest rate caused deflation - which seems like it would certainly happen - then the real interest rate would be above 50%. That would make govt. bonds a much more attractive proposition than the stock market or any other private asset, so it seems like everyone would abandon the real economy and stampede into govt. bonds. with the whole country earning >50% real rates of return, we'd all get rich really quick...this seems physically impossible to sustain for very long.

OK, so you see my problem. I just don't understand the extremes of monetary policy. So instead of making any pronouncements, I want to conduct a pop quiz. This quiz has two short-answer problems. Please answer in the comments, as concisely and succinctly as possible.

Problem 1

Suppose that the Fed targets only one interest rate, a short-term nominal interest rate, and that its only tool is Open Market Operations (it cannot provide any "forward guidance" or communicate with the public at all). Suppose that at date T, the Fed decides to keep the interest rate at zero in perpetuity, and remains unwaveringly committed to this decision for all time > T.

a) Describe the time path of the price level (or inflation/deflation), starting at time T, and going forward to infinity (or until the policy ends).

b) Describe the sequence of Open Market Operations that the Fed will conduct.

Problem 2

Suppose that the Fed targets only one interest rate, a short-term nominal interest rate, and that its only tool is Open Market Operations (it cannot provide any "forward guidance" or communicate with the public at all). Suppose that at date T, the Fed decides to keep the interest rate at 50% in perpetuity, and remains unwaveringly committed to this decision for all time > T.

a) Describe the time path of the price level (or inflation/deflation), starting at time T, and going forward to infinity (or until the policy ends).

b) Describe the sequence of Open Market Operations that the Fed will conduct.

37 comments:

Just a small comment. These models are always in equilibrium. You probably mean something like "far away from the stochastic steady state" or something like that. This is a common confusion, and I think it just adds to sloppy thinking about what equilibrium is in an economic model.

I think you mean that the models are always in short-run equilibrium. In these models there is a short-run equilibrium (in which prices haven't adjusted yet), a long-run equilibrium (in which prices have adjusted), and occasionally a very-short-run equilibrium (in which plans have not yet gone into effect; this is a rare modeling device). The long-run steady state is the long-run equilibrium.

Now that you are a real professor and everything, couldnt you just, you know, email various monetary policy honchos with this pop quiz? Maybe create some kind of fake article you are writing where their responses will be false and you are studying the effect of Fed pronouncements on academics, with an implication for diffusion of future announcements among their students or some other kind of mumbo jumbo with a lot of greek letters.

How I view it is that normally lenders will have a lower propensity to consume than borrowers, therefore 2>1 and lowering interest rates will tend to be potentially more inflationary.

I think the fiscal stance is all important here, since that is what injects net financial assets in non-gov sector. Interest is in that sense "fiscal" policy in that it injects NFA in non-gov sector.

So, its hard to answer your questions without considering the fiscal stance. Setting interest rates to 0% results that aggregate demand should be managed entirely through fiscal policy.

So 1a cannot be answered easily imo without considering other factors.

1b: Easiest way is to not pay IOER (set IOER at 0%) and oversupply reserves.

2a: I think initially this would be deflationary, because credit gets choked off and there is a great incentive to save and reduce debt. However, at a certain point pvt credit has come to a halt, interest income is so high and productive capacity has suffered from the previous period of insufficient aggregate demand, that interest income can very well begin to exceed non-gov sector desired saving rate, which will be in the end be very inflationary. So I go out on a limb and predict at first a deflationary path which results in destruction of productive capacity, and in the end turns into (very) high inflation due to high levels of interest NFA creation and the collapse of productive capacity. Possibly ends in hyperinflation.

b: Either forecast reserve demand and set lending rate at 50% or oversupply reserves and pay IOER at 50%

Kocherlakota: isn't that just reverse logic? What's puzzling in believing that Mr Kocherlakota can make such a blunder?(by the way, I doubt you can have a "safe" investment yielding 1% if the FED rate stays at 0-25 bp)

Problem 1:That's basically making money freely available to commercial banks (that would still charge an interest to borrowers). How the inflation reacts depends upon the demand from borrowers, which in turns depends upon the real rate of return (which depends on growth, which depends on demand from the borrowers).Inflation is not certain in the short run (if growth is very low) but it could spiral rapidly as any inflation would mean negative real rates for borrowers .

Problem 2:That's basically making money unavailable for banks. With a fix supply of money, either deflation must compensate for growth, or people turn to alternative currencies.

Whatever worth are my answers, I always found that reasoning with extremes was one of the more efficient ways of thinking about economic mechanisms. Well done!

Kocherlakota's argument is indeed weird. The whole point of setting nominal short term interest rates is that those rates arbitrage with other rates. Basically, interest on excess reserves arbitrages with very short term gov paper (that's why treasury bills have such a low yield).

So basically, the assumption that there are SAFE investments yielding 1%, while FFR is at 0% seems like a weird assumption (and would be arbitraged away. And if that assumption is wrong, his whole argument collapses.

If the CB's interest rate target is truly permanently fixed, then anything can happen. In a way, it's like the monetarist idea of fixing the monetary base. There's no feedback.

So forget that. A more meaningful question is, suppose somebody told you that the Fed Funds rate was at 0%/50% for 20 years, what would you guess was the realized inflation? And the answer is perfectly clear. About 0%/50%!

If Fed tries to keep inflation bellow the natural rate the economy will inflate, then hiperinflate, then they can't do it anymore. So to keep interest 0 they have to keep the natural rate down.

And he doesn't talk about high rates, so I'll add something:

If they keep it above the natural rate, nominal growth will fall, and fall, making the gap higher and higher, deflating, eventually hiperdeflating until there's only one dollar left, which is worth the whole US economy.

Of course if prices are sticky this wound't be this pretty, production would fall, and fall, and fall until people just rise up and killed the fed. Or reimpose the monetarization of silver. Or just create or start accepting other money.

They could change the natural interest rate to 50% though, by credibly promising to inflate like there will be no tomorrow, making peoples demand for securities rise to the roof.

It's a bit confusing when you say both that there is no forward guidance and that the Fed is "unwaveringly committed" to pegging the interest rate. I suppose this means it is unwaveringly committed but no one else knows that it is unwaveringly committed. I assume no fiscal policy, so there are no taxes or government spending.

1a. Once the market figures out that the Fed is pegging the interest rate at zero forever, the price level jumps to infinity, i.e. the currency becomes toilet paper and people cease using it as money.

1b. The Fed starts by buying Tbills to push the short interest rate to zero. Once the market figures out that the Fed is pegging zero interests forever, both money and nominal bonds become worthless and normal open-market operations become pointless.

2a. Once the market figures that the Fed is pegging interest rates at 50% forever, the price levels falls to near zero (there is a need to assume some type of long-run anchor for the price level to avoid indeterminacy). During this deflationary period there is a great depression. After equilibrium is restored, prices are expected to rise by close to 50% p.a. to keep real rates at equilibrium levels.

2b. The Fed sells enough assets to cut the monetary base to almost zero as there is a mad rush to buy bonds from the Fed at an incredibly attractive 50% yield during a brief period of massive deflation. After equilibrium is restored, expected inflation is very high (just under 50%), money demand is tiny but then so is the money supply. From this point (if civilization has not yet collapsed) everything proceeds swimmingly with everyone adjusting to near-50% inflation.

You will note a lack of symmetry between my answers to Problems 1 and 2, as the price level does not fall to zero with money becoming infinitely valuable in the latter case. I believe that formally such an equilibrium is possible (it may be in Woodford somewhere) but I can't tell a plausible story as to how such a "hyperdeflation" can happen, as I can with hyperinflation.

By contrast, the "Friedman rule" equilibrium of zero interest rates with gentle deflation is so unstable that I can't see how you can get there by pegging nominal rates at zero, at least starting from a "normal" positive level.

At the risk of appearing to be talking to myself, here is an elaboration on further reflection. It seems to me that there are two equilibria in each case, assuming that we start with interest rates at some "normal" level of great than 0% but less than 50%.

In Problem 1, the 0% case, there is an explosive equilibrium which is hyperinflation with money becoming worthless, and a bounded equilibrium which is where the inflation halts and is followed by a gentle deflation consistent with the Friedman rule.

In Problem 2, the 50% case, there is an explosive equilibrium which is "hyperdeflation" with money becoming infinitely valuable, and a bounded equilibrium which is where the deflation halts and is followed by high inflation of a bit less than 50%.

My intuition told me to pick the explosive equilibrium in Problem 1 but the bounded equilibrium in Problem 2. The way to make this happen is to assume that there is a kind of one-way long-run anchor to the price level that prevents it from falling to zero but does not prevent it from going to infinity. I don't really have a good justification for this, other than 1) the fact that we have observed hyperinflations in the real world but no hyperdeflations, and 2) the notion of a zero price level is kind of nonsensical as it must also mean a zero money supply, since otherwise he who owns a single penny can command the entire economy.

I can't see exactly how we would fall on the bounded equilibrium in problem two.

How can the deflation and high interest rates cause inflation to reach 50%? I understand that if nominal growth somehow reached 50% there would be an equilibrium, but not how that could follow from the premises.

Also I just realized i have the same problem with the bonded equilibrium in Problem 1.

1. a) Monetary policy would be fixed by definition according to the fixed policy rate. Fiscal policy would be used in the attempt to manage the price level, whatever the effect of monetary policy. The true and applicable and relevant “real rate” would be determined by credit spreads over the nominal zero risk free rate set by the Fed. Ignore the real rate on zero or near zero nominal interest Treasury obligations, which might well be negative, depending on fiscal policy ease.

b) Open market operations are a non-issue. Set aside the current QE environment of chronic excess reserves. Assume a pre-2008 “normal” monetary environment. Then the Fed manages the supply of excess reserves in a very narrow zone where the demand is completely inelastic. Have a look at the long term series for excess reserves for proof of this. There is no net OMO requirement to speak of. That’s true of all settings for the Fed target rate, pre-2008.

2. The FOMC is put on a bus (if they haven’t already been for attempting policy # 1).

First of all, there is no rate at which you can hold policy constant and have a stable equilibrium. The real rate will almost surely be either above or below the natural rate, which will cause positive, not negative, feedback. So not now, not "in the long run" either.

Problem 1:

I'm assuming you are intending inflation here, i.e. that the *nominal* natural rate is above zero. Because it *could* be a deflation scenario if, say, the natural rate curve is constant at 2% and forward inflation is constant at -3% (nominal natural rate at -1%). Also, the commitment is "unwavering," but nobody knows about it, right? (No forward guidance). Since that effects the shape of the yield curve, it could determine which disequilibrium we end up in. Again, I'm assuming an eventual (hyper) inflationary scenario.

So... accelerating hyper-inflation sets in. Banks lend like crazy at 0%+cost because that's their cost of funding and there is little chance of borrower default. So bank balance sheets explode. So what happens to reserves? Required reserves will increase and the Fed will provide them in exchange for t-bills as usual, but required reserves have no economic consequence. Excess reserves will be whatever the Fed wants them to be. It doesn't matter when FF=IOR. But they could presumably be kept a tiny fraction of M0. If the system is efficient, like LVTS in Canada, no excess reserves are required. But as borrowing raises demand and thereby the price level, the quantity of demanded currency would follow. Again, the Fed would provide it in exchange for t-bills. If they decided not to provide it, the policy rate would rise, as banks collectively try, and fail, to get more reserves in the fed funds market. But note that the price level doesn't *follow* the increase in currency. Lending rates drive demand drive the increase in the base (ignoring required reserves). In a system such as Canada's, with no required reserves, this is bleedingly obvious.

Will this process every end? The process ends when people run out of extra wheelbarrows (then we start using wheelbarrows for money). After that, paper dollars will be worth their weight in old newspapers. Deposits will be worthless.

Problem 2:

Lets assume IOR=0 (not that it matters, but we have to assume something - we can do IOR=FF later if you want). So...

The fed announces 50% policy rate. As it becomes clear that they mean to keep it there *forever*, all investment completely stops as everyone hoards t-bills and deposits, and pays off loans. Nobody borrows. Since all non-essential consumption ends too, a general glut ensues. GDP and the price level plummet. Almost all currency is deposited and then converted to reserves by the banks. Since the banks don't want the IOR=0% reserves they get in exchange, they lend it in the fed funds market. In order to keep the fed funds rate from collapsing, the Fed must take back all those reserves through OMO repos, exchanging them for 50% t-bills which *everyone* wants. There will be zero excess reserves in the system.

Borrowers are in huge trouble, selling assets that nobody wants trying to repay loans. The asset side of banks balance sheet piling up with houses, equipment and other worthless real assets. Panicking depositors try to exchange their deposits for t-bills and commodities. Meanwhile, tax revenues are also plummeting putting the ability of the government to meet its liabilities in serious jeopardy. Banks, governments, and the 99% default.

This answer is based on the New Keynesian model and the phase diagrams of the linearized equilibrium conditions, as exposed in this paper:http://dl.dropbox.com/u/125966/zero_bound_2011.pdf

1. If i=0 during normal times (when the real rate should be positive) then we have a phase diagram similar to Figure 5. If i=0 is expected to be set forever there are multiple bounded possible paths for the economy. The equilibrium is indeterminate. This is a common feature of these models when interest rates are fixed. All the equilibria travel on a (saddle) path that converges to the steady state with negative inflation and output, but the initial starting point is arbitrary. We conclude that all equilibria involve deflation in the long run, but could have substantial inflation in the short run.

Now if we "refine" this exercise by assuming that at some very very distant date T'>T we expect the Fed to fix this situation and go back to, say, zero inflation, then this pins down a unique equilibrium, described by a path converging to the origin and hitting it exactly at T'. For any T' the solution then always entails inflation. This jives better with your intuition that zero interest rates should lead to inflation.

2. The analysis is similar: if i=50% forever (and the "natural" real interest rate is lower) we have a phase diagram similar to Figure 6 and again have multiple equilibria along a saddle path going to the crossings of both blue lines. All equilibria involve inflation in the long run, but could have deflation in the short run. If we refine things by setting a date T' at which things are normalized to somehow obtain zero inflation thereafter then the unique equilibria involves deflation throughout the episode with i=50%.

For part b in both cases one has to compute money demand using M/P=L(y,i) at each point in time. We have already computed inflation so we have P at each date, so this gives us M at each point in time. Open market operations are then described by the change over time in M. Clearly at the steady states with inflation (deflation) we have money growing (contracting) at the rate of inflation (deflation).

In the transitions with our T' refinements we find that output is falling, so M/P is falling (since i is constant). So P is growing while Y is falling, which makes the effect on M indeterminate. Near the steady state, however, inflation is near zero but Y is still falling, so M falls near T'.

look at japan, isn't this about real rates.. set your rates at zero and in the long run it's deflationary. i think both cases have opposite effects in short run vs. the long run as policy impacts run counter to expectations once they are embedded in peoples' minds. *i think* it's always an expectations game (get it, HA!). I'm also sympathetic to fiscal responses playing a very important impact on this dynamic. If govt spends like mad at zero bound, eventually it's very inflationary.. my only argument to that though, is again... LOOK AT JAPAN!!!

1a Assuming that hoarding is risk free and costless, policy rewards gvt bonds holders, inject money in economy once and for all. Thereafter, gvt bonds turns to be useless. Inflation occurs for a time (if economy is at full employment) and then flat.

1b Fed will buy bonds until there are no bond left to buy.

2a If Fed could implement this policy, nearly all savings goes to gvt bonds, private investment collapses. If gvt supplied economy with public investment, probably the return of the investments would be less than 50% yoy and then fiscal budget worsens, gvt would have to give up policy. If gvt did nothing, economy collapses, deflation occurs, fiscal budget worsens, gvt will have to give up policy.

2b Fed will sell bonds and keep selling to mantain target interest rate until balance sheet is empty or reversal of policy.

I'm way less qualified than you, but hey, I read some blogs, so here's a shot (please, professor, give me a passing grade! I promise, as you will be able to tell, that I didn't look at the answers of the smarter kids before responding):

1.A. Undefined. The price level depends on factors other than specified rate. The zero rate may be too tight (i.e., lead to deflation) or too loose (i.e., lead to inflation) depending on factors outside the Fed's control (i.e., "demand for base money" or "demand for dollar denominated safe assets").

1.B. The Fed buys enough short term assets to drive the price up until the yield is zero, and then either buys or sells more of those assets to maintain the zero yield.

2.A. Same as 1.A.

2.B. Um. I guess it sells assets until yields reach the desired level, although I don't know where it gets the assets to sell.

Problem 1. People now expect near 2% inflation. Presumably they will keep expecting this until something happens to change their mind. What might happen, and how would it change their mind?

Most likely, I think: the adult population keeps growing (as it will for the next 15 years with near 100% probability) and eventually the rising demand for housing causes rising rents and home prices and a boom in construction, as well as consumption via mortgage equity withdrawal, along with the associated multiplier effects. Eventually the associated increase in aggregate demand uses up all easily available labor and starts to bid up prices. People notice that the Fed is not raising rates despite an increase in the inflation rate. As more and more people realize that the Fed is not going to raise rates, they come to expect a higher inflation rate, and you get Friedman-Phelps-Lucas effects. So the inflation rate just keeps rising. Eventually people realize that the Fed is never, ever going to raise rates, and you get hyperinflation.

Another possibility: Profit margins are very high right now, on average. Maybe firms will start competing aggressively and prices will fall. And since there's high unemployment, once they compete away those profits, maybe they will start cutting wages. So you get deflation. This raises the real interest rate and makes investment less attractive, which reduces demand, which accelerates the deflation, so you get a deflationary spiral. Note however, that this deflationary spiral would happen no matter what the Fed does with interest rates. Also note that it seems intuitively kind of implausible that we could have a bubble in the value of money that never pops. So if I had to choose, I think that my first possibility is much more likely -- at least it's more likely to be the eventual endgame, although you could get some temporary deflation along the way.

Problem 2. Given the Fed's current asset base, the only way it could keep the interest rate at 50% is by paying 50% interest on reserves. That would effectively suck nearly all the money out of the economy, because banks would stop lending and start bidding aggressively for deposits. But it would all be funny money, because the Fed's net worth would go ever deeper into negative territory. (It's assets are mostly longer duration assets that would lose most of their value if the 50% interest rates were expected to persist.) It's hard to say what the endgame would be. Maybe extreme deflation and increasing use of alternative means of payment. Or maybe not, maybe people would lose confidence in money -- these credits the Fed would be making without anything to back them up -- and we would get inflation instead.

I don't think we can get rich by increasing risk free yield. Not any more than we can violate the laws of thermodynamics.

At that interest rate, financial assets drop in price such that the overall yield is identical to what you would have had in the first place. So the only folks who could benefit from this would be from those with cash. But by raising the interest rate above natural rate of return, at equilibrium, you get deflation such that cash would have a 50% effective yield anyway. Or something like that.

I'm not certqin this Kocherlakota person understands the difference between the Fed Funds rate and a support/maintenance rate.

The Fed Funds rate is determined by open market operations, the Fed altering the composition of net financial assets so as to hit a target overnight rate. But this isn't what keeps the interbank rate at 0.25%. The interbank rate wants to fall to zero because banks have large quantities of excess reserves on their balance sheets not earning a return (excess reserves are just that: an excess of what a given bank needs). What prevents this from happening is the support rate of 0.25% being paid out by the Fed on excess reserves. The entire point of a support rate is to establish a floor for the price of reserves, while the penalty rate of the Fed's discount window creates a ceiling.

The scenario quoted above bears no resemblance to these policies, rendering the whole thing not only a meaningless excercise, but a little absurd.

JHK, since you brought up fiscal policy/MMT, you might like this Woodford paper:

http://www.columbia.edu/%7Emw2230/BOE.pdf

"...a policy of trying to peg the nominal interest rate is commonly denounced as a policy that leaves the equilbrium price level indeterminate, and so vulnerable to price-level variations due to self-ful lling expectations (Sargent and Wallace, 1975). This would be correct, according to our model, in the case of a Ricardianfiscal policy. But in the case of an exogenous path for the government surplus, such a policy results in a determinate equilibrium price level, which may involve low and stable inflation."

I realise I'm a bit late to the party, I've been thinking about it for a few days. I don't have answer to the pop quiz, but isn't Kocherlakota's argument a version of the unpleasant arithmetic?

Quoting Sargent’s Macro textbook, section 24.3.4:

"Consider an open market sale of bonds at time 0, defined as a decrease in M1 accompanied by an increase in B, with all other government fiscal policy variables constant... The effect of the policy is to shift the permanent gross-of-interest deficit upward... which decreases the real return on money... That is, the effect is unambiguously to increase the stationary inflation rate (the inverse of Rm). However, the effect on the initial price level p0 can go either way, depending on the slope of the revenue curve...

The effect of a decrease in the money supply M1 accomplished through such an open market operation is at best temporarily to drive the price level downward, at the cost of causing the inflation rate to be permanently higher."

Just invert the argument to get Kocherlakota's conclusion: open market purchase at time 0 decreasing the interest rate can temporarily drive the price level up (creating short-run inflation) but the long run inflation rate is permanently lower.

He didn't express it this way at all though; his seemed to be an argument based on an identity (see: arguing with economists principle 4...)

- We start in equilibrium where all changes in MV will be reflected in changes in the price level in the medium to long term.- There is a natural rate of interest that is the market clearing rate in a scenario of a fixed money supply

To maintain zero rate of interest: The fed sells assets via OMO until it achieves a deflation rate equal to the natural rate of interest. The economy will remain in a liquidity trap and have zero IR, or (best case scenario) adjust to the deflation and a nominal rate of zero will actually be the correct natural real that will achieve equilibrium.

To maintain a 50% rate: Just target inflation of (50% minus the natural IR). if they don't know what natural rate is then just use OMO to increase the money supply when the rate goes above 50% and increase it when it falls below. Short term this policy might drive the IR off target. Increasing the money supply will initially cause IRs to fall not rise, but once the inflation target is hit IR will be easy to target)

Say there are two assets in the economy... reserves at the Fed, and some durable good. Asset holders expect a sufficient return on each asset and will switch between the two should returns diverge. The return on reserves is provided by an interest component plus liquidity, while the return on the good by capital appreciation. Start at the point at which returns are equal. The Fed announces it will reduce the rate paid on reserves to 0%. The price of the durable good must immediately jump to a new price at which it no longer provides as much expected capital appreciation as before.

As more people realize that the 0% returns on reserves will not be temporary, stock prices must move higher each time that this "realization dawns" so as to equilibrate returns. When everyone has discovered the policy, the price of the durable good stops rising. If everyone had figured the policy right off the bat, the price of the durable good would jump immediately to this new higher price.